Almost free algebras have polynomial-time decidable problems for canonical forms, class cardinalities, finiteness checks, and isomorphism, plus quantifier elimination after adding tester predicates via a new approach.
On the algorithmic unsolvability of the word problem in group theory.Proceedings of the Steklov Institute of Mathematics, 44:1–143
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Almost free algebras: from the word problem to elimination of quantifiers
Almost free algebras have polynomial-time decidable problems for canonical forms, class cardinalities, finiteness checks, and isomorphism, plus quantifier elimination after adding tester predicates via a new approach.